Extending the weak order on Coxeter groups

Francois Viard (1, 2)

1 ICJ - Institut Camille Jordan
2 UCBL - Université Claude Bernard Lyon 1

We introduce a new family of complete lattices, arising from a digraph together with a valuation on its vertices and generalizing a previous construction of the author. We then apply this to the study of two long-standing conjectures of Dyer, and we provide a description of the Tamari lattice with this theory.

Mots clés: Combinatorics

Domaines: Combinatoire [math.CO]

Francois Viard. Extending the weak order on Coxeter groups. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6409⟩. ⟨hal-02166056⟩